**MAXIMUM MARKS 35 ** **TIME: 1 HOURS**

1. Compute the amount and the compound interest on Rs 10000 compounded annually for two and half years at 4% per annum.

2. Prove that the quadrilateral formed by joining the midpoints of the adjacent side of a rectangle is a parallelogram.

3.Difference of two perfect cubes is 387. If the cube root of the greater of two number is 8. Find the cube root of the smaller number?

4.A fort is provided with food for 80 soldiers to last for 60 days. Find how long would

the food last if 20 additional soldiers join after 15 days?

5. A gardener has 1400 plants. He wants to plant these in such a way that the number of rows and number of columns remains same. Find the minimum number of plants he needs more for this.

6. A and B together can build a wall in 10 days; B and C working together can do it in 15 days, C and A together can do it in 12 days. How long will they take to finish the work, working all together? Also find the number of days taken by each to do the same work, working alone.

7. Find two consecutive even integers such that two-fifth of the smaller exceeds two eleventh of the larger by 4.

8. The following data represents the number of students got admission in different streams of a college:

Stream | Science | Arts | Commerce | Law | Management |

Number of students | $400$ | $300$ | $500$ | $250$ | $350$ |

Draw a pie chart to represent this data.

9.One of the diagonals of a rhombus and its sides are equal find the angles of the rhombus.

10.A wall hanging is marked for Rs 4800. The shopkeeper offers 10% discount on it if GST is received 8% from the customer find the amount paid by the customer to purchase the wall hanging.

11.Find the smallest square number which is divisible by each of the numbers 6 , 9 and 15.

12. Find the greatest number of 5 digits which is a perfect square.